Tough and tricky: The sum of the even numbers.

We're looking at the sum of even numbers between 1 and k, with k being an odd number. So essentially, we're looking for the sum of even numbers between 2 and (k-1).

Sum (in consecutive series) = Average * Number of Elements in Subset

Average \(= \frac{2 + (k-1)}{2}\)

Number of Elements in Subset\(= \frac{k-1}{2}\)

Sum \(= [\frac{2 + (k-1)}{2}][\frac{(k-1)}{2}]\)

\(= [\frac{(k+1)}{2}][\frac{(k-1)}{2}]\)

\(= [\frac{(k+1)}{2}][\frac{(k+1)}{2} - 1]\)

It's easy to see that these two terms are consecutive digits. We know that the sum is equal to 79*80, and therefore we can solve for k.

\(80 = \frac{k+1}{2}\)

\(160 = k + 1\)

\(k = 159\)

Therefore, the correct answer is E:159.